code: def test_computes_piecewise_polynomial_kernel(self):
      a = torch.tensor([[4, 1], [2, 2], [8, 0]], dtype=torch.float)
      b = torch.tensor([[0, 0], [2, 1], [1, 0]], dtype=torch.float)
      kernel = PiecewisePolynomialKernel(q=0)
      kernel.eval()
  
      def test_r(a, b):
          return torch.cdist(a, b)
  
      def test_get_cov(r, j, q):
          if q == 0:
              return 1
          if q == 1:
              return (j + 1) * r + 1
          if q == 2:
              return (
                  1
                  + (j + 2) * r
                  + ((j**2 + 4 * j + 3) / 3.0) * r**2
              )
          if q == 3:
              return (
                  1
                  + (j + 3) * r
                  + ((6 * j**2 + 36 * j + 45) / 15.0) * r**2
                  + ((j**3 + 9 * j**2 + 23 * j + 15) / 15.0)
                  * r**3
              )
  
      def test_fmax(r, j, q):
          return torch.max(torch.tensor(0.0), 1 - r).pow(j + q)
  
      actual = torch.zeros(3, 3)
      j = torch.floor(a / 2.0).shape[-1] + kernel.q + 1
      r = test_r(a, b)
      actual = test_fmax(r, j, kernel.q) * test_get_cov(r, j, kernel.q)
      res = kernel(a, b).to_dense()
      self.assertLess(torch.norm(res - actual), 1e-5)
  
      # diag
      actual = actual.diagonal(dim1=-1, dim2=-2)
      res = kernel(a, b).diagonal(dim1=-1, dim2=-2)
      self.assertLess(torch.norm(res - actual), 1e-5)
  
      # batch_dims
      actual = torch.zeros(2, 3, 3)
      for i in range(2):
          actual[i] = kernel(
              a[:, i].unsqueeze(-1), b[:, i].unsqueeze(-1)
          ).to_dense()
  
      res = kernel(a, b, last_dim_is_batch=True).to_dense()
      self.assertLess(torch.norm(res - actual), 1e-5)
  
      # batch_dims + diag
      res = kernel(a, b, last_dim_is_batch=True).diagonal(
          dim1=-1, dim2=-2
      )
      actual = torch.cat(
          [
              actual[i].diagonal(dim1=-1, dim2=-2).unsqueeze(0)
              for i in range(actual.size(0))
          ]
      )
      self.assertLess(torch.norm(res - actual), 1e-5)
  
file_path: gpytorch/test/kernels/test_piecewise_polynomial_kernel.py
imports: import unittest
  import torch
  from gpytorch.kernels import PiecewisePolynomialKernel
  from gpytorch.test.base_kernel_test_case import BaseKernelTestCase
label_desc: Use image node_id 2 for calling the TestPiecewisePolynomialKernel obj's underlying member method code with example usage: obj.test_computes_piecewise_polynomial_kernel() and returns: torch, torch, int, unknown, unknown, unknown